Exact mobility edges for 1D quasiperiodic models

Abstract

Mobility edges (ME), i.e. critical energies which separate absolutely continuous spectrum and purely point spectrum, is an important issue in quantum physics. So far there are two experimentally feasible 1D quasiperiodic models that have been discovered to have exact mobility edge. However, all the theoretical studies have remained at the numerical level. In this paper, we rigorously prove the existence and give the precise location of the MEs for these models.

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• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Arithmetic Phase Transitions For Mosaic Maryland Model
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Types of dynamical behavior in a quasiperiodic mosaic lattice